函数y=lg(sinx-cosx/sinx+cosx)的定义域 HELP!>oo

函数y=lg(sinx-cosx/sinx+cosx)的定义域 HELP!>oo
函数y=lg(sinx-cosx/sinx+cosx)的定义域 HELP!>oo

函数y=lg(sinx-cosx/sinx+cosx)的定义域 HELP!>oo
(sinx-cosx)/(sinx+cosx)>0
cosx=0,显然为解,x=kπ+π/2
cosx0,(tgx-1)/(tgx+1)>0---> tgx>1 or tgx kπ+π/4

(sinx-cosx) / (sinx+cosx) > 0
(sin²x-cos²x) / (sinx+cosx)² > 0 => cos 2x < 0
=> 2kπ + π/2 < 2x < 2kπ+3π/2
=> 定义域: ( kπ + π/4 , kπ+3π/4)